1. Field of the Invention
This invention relates to a multiplier and a squaring circuit to be used for the same and more particularly, to a multiplier including a plurality of squaring circuits having differential input terminal pairs and adapted to be arranged on a bipolar integrated circuit and a squaring circuit to be used for the same.
2. Description of the Prior Art
Conventional multipliers are a Gilbert multiplier in general. The Gilbert multiplier has such a structure that transistor pairs are provided in a two-stage stack manner and a constant electric current source I0 as shown in FIG. 1. The operation thereof will be explained below.
In FIG. 1, an electric current (emitter current) IE of a junction diode forming a transistor can be expressed by the following equation (1), where Is is saturation current, k is Boltzmann's constant, q is a unit electron charge, VBE is voltage between base and emitter and T is absolute temperature. EQU IE=Is.multidot.exp(q.multidot.VBE/kT)-1 (1)
Here, if VT=kT/q, as VBE&gt;&gt;VT, when exp(VBE/VT)&gt;&gt;1 in Eq. (1), the emitter current IE can be approximated as follows; EQU IE.apprxeq.Is.multidot.exp(VBE/VT) (2)
As a result, collector currents IC43, IC44, IC45, IC46, IC41 and IC42 of the transistors Q43, Q44, Q45, Q46, Q41 and Q42 can be expressed by the following equations (3), (4), (5), (6), (7) and (8), respectively; ##EQU1##
In the above equations, V41 is an input voltage of the transistors Q43, Q44, Q45 and Q46, V42 is an input voltage of the transistors Q41 and Q42, .alpha.F is current amplification factor thereof designated by the large signal forward gain for the common base configuration.
Hence, the collector currents IC43, IC44, IC45 and IC46 of the transistors Q43, Q44, Q45 and Q46 can be expressed by the following equations (9), (10), (11) and (12), respectively; ##EQU2##
As a result, the differential current .DELTA.I between an output current IC43-45 and an output current IC44-46 can be expressed by the following equation (13); ##EQU3##
Here, tanh x can be expanded in series as shown by the following equation (14) as; EQU tanh x=x-(x3/3) (14),
so that if x&lt;&lt;1, it can be approximated as tanh x=x.
Accordingly, if V41&lt;&lt;2VT and V42&lt;&lt;2VT, the differential current .DELTA.I can be approximated by the following equation (15); From Eq. (15), it can be found that the circuit shown in FIG. 1 becomes a multiplier for the input voltages V41 and V42 as a small signal. EQU I.apprxeq.(1/4) (.alpha.F/VT).sup.2 .multidot.V41.multidot.V42(15)
In this case, however, the conventional Gilbert multiplier as explained above has transistor pairs stacked in two stages, so that there arises such a problem that the source voltage cannot be decreased.
Next, a conventional squaring circuit formed on a C-MOS integrated circuit obtains a squaring characteristic by using a MOS transistor at the source follower as shown in FIG. 2. The drain current Id thereof can be expressed by the following equation (16) in the saturation region, where W is gate width, L is gate length, VGS is voltage between gate and source, Vt is threshold voltage, .mu.n is mobility of electron, and COX is unit gate oxide film capacity; EQU Id=.mu.n.multidot.(COX/2) (W/L) (VGS-Vt).sup.2 ( 16)
According to Eq. (16), the drain current Id changes with the threshold voltage Vt. The threshold voltage Vt has a variation on a production basis. This means that with the conventional squaring circuit using MOS transistor at the source follower, the drain current Id cannot be made constant even by applying the same gate voltage VGS. As a result, there arises such a problem that the conventional squaring circuit is difficult to be integrated on a large-scale basis.
In consideration of the above-mentioned problems, an object of this invention is to provide a multiplier capable of reducing a source voltage.
Another object of this invention is to provide a squaring circuit which is easy to be integrated on a large-scale basis and which is adapted to be used for a multiplier.